Observing the graph, we see that the values of y decrease as the values of x increase. So, the curve is decreasing. Then, the equation of the line in the slope-intercept form should present a negative slope:
y = ax + b, a < 0
Also, we can see that the graph intercepts the y-axis at a negative value of y. Thus, b (the y-intercept) is also negative:
b < 0
Now, we can rewrite the given equations and analyze which of them satisfies those conditions.
• 3x - y = -2
3x = -2 + y
3x + 2 = y
y = 3x + 2
Since 3 > 0 and 2 > 0, this equation could not belong to the gragh.
• 3x + y = 2
y = -3x + 2
Since 2 > 0, this equation could not belong to the graph.
• 3x + y = -2
y = -3x - 2
Since -3 < 0 and -2 < 0, this equation could indeed belong to the graph.
• 3x - y = 2
3x = 2 + y
3x - 2 = y
y = 3x - 2
Since 3 > 0, this equation could not belong to the graph.
Therefore, only the third option is correct.